SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1148-1171, January 2020.
We address the new problem of designing large families of subsets of a common labeled ground set that simultaneously have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the subsets is less than or equal to one. Our results include an upper bound on the size of such families, and constructions based on transversal designs, packings, and new forms of Latin rectangles. The constructions jointly optimize the size of the family of sets and the labeling scheme and achieve optimal family sizes for many parameter choices. Probabilistic arguments akin to those used for pseudorandom generators lead to significantly suboptimal results when compared to the proposed combinatorial methods. The intersecting sets discrepancy problem is motivated by emerging applications in coding for molecular data storage.

中文翻译：

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具有小交叉点和小差异的设置代码

SIAM离散数学杂志，第34卷，第2期，第1148-1171页，2020年1月。
我们解决了设计共同标记地面集合的大子集族的新问题，这些子集同时具有较小的成对相交，并且每个子集内的标记值的最大差异小于或等于1。我们的结果包括此类族群的上限，以及基于横向设计，包装和新形式的拉丁矩形的构造。该构造共同优化了集合族和标签方案的大小，并为许多参数选择实现了最佳族大小。与拟议的组合方法相比，类似于伪随机数发生器的概率论证会导致明显次优的结果。